Melody of Oblivion... this is one anime that stands in my head as having great songs. Many of them are orchestra based music styles but I still love the songs for this especially the opening 'Will' by Lisa.

Another anime that has good music, Fushigi Yugi... Itooshii Hito no Tame ni by Akemi Satou and Tokimeki no Doukasen by Yakari Konno... I so love it!